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1) Suppose that the cost, P, of shipping 3 pound parcel depends on the distance shipped, x, according to the function P(x) depicted in the graphFind each limit; if...

Question

1) Suppose that the cost, P, of shipping 3 pound parcel depends on the distance shipped, x, according to the function P(x) depicted in the graphFind each limit; if it exists:lim P(x) lim P(x) lim P(x) x-+100 x1500 X-300OL 8[000 2000 Dblance Shlpped (mlloo)

1) Suppose that the cost, P, of shipping 3 pound parcel depends on the distance shipped, x, according to the function P(x) depicted in the graphFind each limit; if it exists: lim P(x) lim P(x) lim P(x) x-+100 x1500 X-300O L 8 [000 2000 Dblance Shlpped (mlloo)



Answers

The cost of sending a large envelope via U.S. first-class mail is $\$ 0.88$ for the first ounce and $\$ 0.17$ for each additional ounce (or fraction thereof). (Source: www.usps.com.) If $x$ represents the weight of a large envelope, in ounces, then $p(x)$ is the cost of mailing it, where $$\begin{array}{l} p(x)=\$ 0.88, \quad \text { if } \quad 0< x \leq 1, \\ p(x)=\$ 1.05, \quad \text { if } \quad 1 < x \leq 2, \\ p(x)=\$ 1.22, \quad \text { if } \quad 2 < x \leq 3, \end{array}$$
and so on, up through 13 ounces. The graph of $p$ is shown below
Using the graph of the postage function, find each of the following limits, if it exists.
$$\lim _{x \rightarrow 3} p(x)$$

Time again. This is the same function, right? And we want to find the limit for two. So what we want to find is limit off P off X when extends two to minus. This is nothing but the elegant and looking at the graph. I am trying to reach two from the left hand side and I'm going to get the value 1.5 So this is 1.5 Similarly, from the graph, I can say that limit off P off eggs for extents to two plus extents. 22 Plus, this is going to be from the graph. I can see that this will be 1.22 This is 1.22 and hence Aiken say that since a little and Rachel are not equal limit off P affects when extends to do does not exist, this does not exist. And this would be my answer

Time again. This is the same function, right? And we want to find the limit for two. So what we want to find is limit off P off X when extends two to minus. This is nothing but the elegant and looking at the graph. I am trying to reach two from the left hand side and I'm going to get the value 1.5 So this is 1.5 Similarly, from the graph, I can say that limit off P off eggs for extents to two plus extents two plus, this is going to be from the graph. I can see that this will be 1.22 This is 1.22 and hence Aiken say that since a little and Rachel are not equal limit off P affects when extends to do does not exist, this does not exist. And this would be my answer

All right, this is the graph. We have to find the limited 3.6. So that's why we have also run this. One more body can see Upstairs we have this extended this crab. Now, now we want to find Let's try to find the electoral and let's l means nothing. But when extends to 3.6 minus what is this going to be from the graph? I can see that this is going to be 3.6 will fall somewhere around here in the between right over here in the between. And this is 1.39 Similarly, the NHL is also 1.39 This is 1.39 Similarly, the origin are h ell or when I say that my ex tends to 3.6 distance to 3.6 plus even this is 1.39 Both of these are equal, right? Both off. These election and original are equal and finite. So I can say that my limit off p off X. When my extends to 3.6, this is going to be 1.39 it exists, and this is 1.39 and this would be my answer

Let us look at the function that we have. We have a function P off eggs. Okay, This is a kind of peace wise function. 0.88 The good thing is that all of these are constants. 0.88 1.5 and 1.21 point 05 and 1.22 Okay. And where do these break zero and 11 and 22 and three. Okay, zero and one. One and two, two and three. Is this great? Yeah. And we need to graph this. So let's say that this is a graph. Let's say that this is our graph between zero and 10.8 in and zero is not included. So this is 0.88 between zero and one. This is one. This is 0.88 between one and two. It has 1.5 Okay, this is between one and two. This is 1.5 and between two. And three. This is 1.22 between two. And three. This is 1.22 All right, So this is my craft, right? This is my graph. What do we need to find minus one? Sorry. One minus one plus and extends to one. Okay, so limit off P off eggs when extends to one minus. What happens in this case? I'm reaching toe one from this side again. I keep on walking. And where exactly do I reach At zero. Find a date. So this is 0.88 limit off P off X when extends to one. Plus. What is this? I'm trying to reach one from the right hand side. So this thing where we reach I am reaching at 1.5 Okay, so at 1.5 this is 1.5 Now, this is the militant or the left hand limit. This is the original or the right hand limit. Both of them, our finite. But they're not equal. So I will say that limit off P off eggs at extending to one does not exist does not exist. And this is my answer for this question.


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